Which point lies on a circle that is centered at a(-3, 2) and passes through b(1, 3)?

c(-1, -2)

d(-6, 3)

e(-3, -3)

f(-2, 6)

 The point that lies  on the circle is (4) F(-2, 6).

Step-by-step explanation: We are to select the correct point that lies on a circle that that is centred at A(-3, 2) and passes through B(1, 3).

The standard equation of a circle with centre at (g, h) and radius 'r' units is given by

The centre of the given circle is A(-3, 2), so we have

(g, h) = (-3, 2).

Also, the circle passes through the point B(1, 3).

Substituting these values in equation (i), we get

Therefore, the equation of the circle with centre (-3, 2) and radius √17 units is given by

Thus, the required equation of the circle is

Option (1) is  C(-1, -2).

We have

So, the point C lies outside the circle.

Option (2) is  D(-6, 3).

We have

So, the point D lies inside the circle.

Option (3) is  E(-3, -3).

We have

So, the point C lies outside the circle.

Option (4) is  F(-2, 6).

We have

So, the point F lies on the circle.

Thus, the point that lies  on the circle is F(-2, 6).

Option (4) is correct.

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step-by-step explanation: